| 摘要: |
| 本文研究了二维扩散方程九点格式中节点辅助未知量的插值问题. 基于线性精确准则,
利用多点通量逼近的边未知量插值算法和一个特殊的极限技巧, 获得了节点辅助未知量的一个新的插
值算法, 并在给定假设下严格分析了该算法中局部线性系统的可解性, 最后用数值算例验证了算法的
有效性. |
| 关键词: 扩散方程 九点格式 线性精确 节点未知量插值 |
| DOI： |
| 分类号:O241.82 |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
|
| A NEW NODAL INTERPOLATION ALGORITHM IN NINE POINT SCHEME FOR DIFFUSION PROBLEMS |
|
Dong Cheng1, Wu Ji Ming2
|
|
1.Graduate School of China Academy of Engineering Physics;2.Institute of Applied Physics and Computational Mathematics, Beijing
|
| Abstract: |
| In this paper, we discuss the interpolation problem for nodal auxiliary unknowns
in nine point scheme for 2D diffusion problems. Based on linearity-preserving criterion and
by applying a special limit technique to the edge interpolation algorithm in multipoint
flux approximation, we obtain a new nodal interpolation algorithm. Moreover, the solvability of the
local system in the interpolation algorithm is analyzed rigorously under certain assumptions.
Numerical results are also provided to validate the efficiency of the new algorithm. |
| Key words: diffusion equation nine point scheme linearity preserving nodal interpolation |
